On nonlinear profile decompositions and scattering for a NLS-ODE model

Scipio Cuccagna; Masaya Maeda

On nonlinear profile decompositions and scattering for a NLS-ODE model

Analysis of PDEs 2018-06-27 v4

Authors: Scipio Cuccagna , Masaya Maeda

Abstract

In this paper, we consider a Hamiltonian system combining a nonlinear Schr\" odinger equation (NLS) and an ordinary differential equation (ODE). This system is a simplified model of the NLS around soliton solutions. Following Nakanishi \cite{NakanishiJMSJ}, we show scattering of $L^2$ small $H^1$ radial solutions. The proof is based on Nakanishi's framework and Fermi Golden Rule estimates on $L^4$ in time norms.

Keywords

nonlinear schrödinger equation scattering theory

Cite

@article{arxiv.1701.02849,
  title  = {On nonlinear profile decompositions and scattering for a NLS-ODE model},
  author = {Scipio Cuccagna and Masaya Maeda},
  journal= {arXiv preprint arXiv:1701.02849},
  year   = {2018}
}

Comments

33 pages

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